Formation fluid is often extracted from a subterranean formation to test and/or analyze characteristics of the formation fluid. A drill string including a downhole tool or a formation sampling tool may be disposed in a borehole. During a sampling operation, the formation fluid extracted from the subterranean formation enters the formation sampling tool. After the formation fluid is tested and/or analyzed, the formation fluid may be stored in the tool and/or discarded into an annulus region between the outside of the drill string and the wall of the borehole. Also, during the sampling operation, wellbore fluid may be pumped into an interior of the drill string. The wellbore fluid may flow downwardly through the drill string and may exit the drill string via ports in a drill bit. The wellbore fluid may then circulate upwardly through the annulus region.